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Results tagged with elliptic-curves
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user 37644
An elliptic curve is an algebraic curve of genus one with some additional properties. Questions with this tag will often have the top-level tags nt.number-theory or ag.algebraic-geometry. Note also the tag arithmetic-geometry as well as some related tags such as rational-points, abelian-varieties, heights. Please do not use this tag for questions related to ellipses; instead use conic-sections.
16
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Is every $GL_2(\mathbb{Z}/n\mathbb{Z})$-extension contained in some elliptic curve's torsion...
I suppose this question could be phrased in terms of Galois representations, but I'm asking it this way.
Let $n>1$ be an integer. If $K$ is a number field with $\operatorname{Gal}(K/\mathbb{Q}) \c …
- 1,499
15
votes
1
answer
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What are the strongest conjectured uniform versions of Serre's Open Image Theorem?
This question concerns the uniform conjectured effective versions and generalizations of these two results of Serre on $\ell$-adic Galois representations $\rho_{E,\ell}$ associated to a non-CM ellipti …
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5
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Order of torsion group
Extended comment. OP Asked if there was an easy way to see that the group is finite. Indeed, if $E$ is an elliptic curve over $\mathbb{Q}$ and $K$ is a Galois extension of $\mathbb{Q}$ with only fin …
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4
votes
1
answer
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Are elliptic Kummer extensions big?
Loosely speaking, are elliptic Kummer extensions big? More concretely:
Let $E$ be an elliptic curve over $\mathbb{Q}$, let $p$ be a prime, and
let $F$ be a subfield of $\overline{\mathbb{Q}}$ contai …
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